By using the boundary layer function method, we studied the internal layer problems of a class of singularly perturbed Hamiltonian systems,  obtained a uniform asymptotic solution for this type of problem, and  proved the existence of the stepwise solution and the uniform validity of formal asymptotic solutions by using the method of ‘sewing’.

Let A be a factor von Neumann algebra acting on a Hilbert space H with dim H >1. With the help of method of algebraic decomposition, we prove that if a nonlinear map δ: A→A satisfies (A·B·C)=(A)·B·C+A·(B)·C+A·B·(C) for any A,B,C∈A, then  is an additive *derivation.

Let (X,d,μ) be a nonhomogeneous metric measure space satisfying the upper doubling and the geometrically doubling conditions. For a class of MorreyHerz spaces on the nonhomogeneous metric measure spaces, by using the properties of the nonhomogeneous metric measure spaces and the theory of boundedness for singular integral operators on the L^p spaces, we proved the boundedness of the Marcinkiewiczintegral operator and its commutator generated by RBMO function on the Morrey-Herz spaces with nonhomogeneous metric measure.

By applying the method of weight functions and HermiteHadamard’s inequality, we established a halfdiscrete Hilberttype inequality with the nonhomogeneous kernel of more accurate strengthened version, and gave a group of equivalent properties of the best constant factor related to a few parameters and some particular inequalities.

We established some inequalities of generalized normalized δ-Casorati curvatures for submanifolds in a Sasakian sta
tistical manifolds with constant sectional curvature, and gave the condition for the equality sign to hold.

Using the method similar to the circuit axioms of matroids, we discussed fuzzy circuit axioms of closed GV fuzzy matroids. 
Firstly, we gave some  properties of fuzzy circuits of G-V fuzzy matroids. Secondly, using these properties, we discussed how to use elementary fuzzy circuit sets to determine G-V fuzzy matroids. Finally, we proposed and proved a fuzzy circuit axiom of closed G-V fuzzy matroids. According to  this  axiom,  a collection of elementary fuzzy sets, a finite number sequence and a mapping of fuzzy sets could  uniquely determine a closed G-V fuzzy matroid under certain conditions.

Using the uniform estimates of the solution and the operator decomposition technique, the author investigated extensible suspension bridge equation with additive noise and linear memory, and proved the existence of its random attractors.

By using Schauder fixed point theorem and contracting mapping principle, we studied the existence and uniqueness of solutions
 for integral boundary value problems of a class of fractional functional differential equations with impulses, obtained and proved the theorems of existence and uniqueness of solutions for the integral boundary value problems, and gave an example  to illustrate the applicability and validity of the conclusions.

We used the method of energy estimate and the comparison principle to establish the theorem of Fujita type for the homogeneous Neumann exterior region problems for a class of nonlinear coupled convectiondiffusion systems. We determined the critical Fujita curves that described whether solutions existed globally or not, and described the influence of the spacial dimension, convection and reaction terms of the systems on the longterm asymptotic behavior of the solution.

Using the Chebyshev expansion block instead of  the hidden layer structure, we proposed a method of Chebyshev neural network model based on function approximation to solve nonlinear Fredholm integral equations, and gave its best  approximation solution and the convergence analysis of the algorithm. The feasibility and effectiveness of the algorithm were verified by numerical examples.

We discussed the stability problem of a repairable system with two different failure modes by using operator semigroup theory. By  transforming the system model into an abstract Cauchy problem, we analyzed the distribution of spectral points of system operators, and  proved that  spectral points of system operators were all located  in the left half plane of the complex plane, and there were no spectral points  on the imaginary axis expect for 0 point. Furthermore, we gave the 
 asymptotic stability of the system solution. Finally, we analyzed the steadystate indices of the system from the perspective of eigenvector.

Using  the design idea of  the structure of graphs and number theory, the graph labelling was  applied to the  graphical cryptograph. The hierarchical cascade graph was used as the basic graph, which was  connected with cycle graph to  construct a unicyche graph, and then the two hierarchical cascade  graphs were overlapped to construct the twin vertex overlap graph. We proved that it has set-ordered odd-elegant labellings, odd-graceful labelling and set-ordered odd-graceful labelling.

By using contradiction, the method of combinatorial analysis and the method of constructing specific coloring, we discussed the vertex-distinguishing E-total (VDET) coloring of complete bipartite graph K_9,n(9≤n≤92),  gave the optimal VDET coloring of complete bipartite graph K_9,n(9≤n≤92), and obtained the VDET chromatic number of K_9,n (9≤n≤92).

First, the perfect matching of graphs 3-nY₄ and 3-nC_6,3 was classified according to the perfect matching of a certain vertex, we obtained  a set of recursive formulas which were related to  each other. Then,  the formula for calculating the perfect matching number of these two kinds of graphs was derived from the relationship between the recursive formulas.

Aiming at the problem that the first frame needed to be manually selected and the subsequent tracking interference was caused by selection deviations in the spatiotemporal context tracking algorithm, we proposed to use Adaboost algorithm to detect the first frame and introduce Kalman prediction mechanism to assist spatiotemporal context tracking algorithm. When occlusion, jitter and other problems occurred, it could ensure the stability of tracking and improve the robustness of the  algorithm. Comparative experiments were carried out on three public data sets, such as Shelter1. The experimental results show that the proposed algorithm can realize the automatic detection function of the first frame, and the robustness 
and tracking effect of the subsequent tracking algorithm are also significantly improved.

Aiming at the problem that the current fuzzy region judgment algorithm in network intrusion did not consider the selfadaption and faulttolerance of the algorithm, and had the disadvantage of poor judgment efficiency and stability, the author proposed a fuzzy region judgment algorithm in network intrusion based on multilayer logic structure. Firstly, 
the fuzzy region judgment algorithm based on multilayer logic structure was adopted,  the selfadaption and faulttolerance were taken as constraints, and the fuzzy region judgment results in network intrusion were obtained by calculating the feedback solutions of different layers of the algorithm. Secondly, based on the judgment results, the alarm synthesis algorithm was used to synthesize many identical alarms into an alarm to prevent the formation of alarm flood and obtain the best fuzzy region judgment results. The experimental results show that the total average detection rate and false alarm rate of the proposed algorithm are 9313% and 097% respectively, and the average time is 1013 s, which shows that the proposed algorithm has remarkable advantages in judging the fuzzy area of network intrusion.

Aiming at the characteristics of lung CT data with spatial information, we proposed a twostage method based on deep learning for the detection and classification of pulmonary nodules in CT images. Two 3D convolution networks were used to effectively learn nodule features. For the detector part of the method, a 3D semantic segmentation model was designed for nodule detection with a UNetlike encoderdecoder structure to predict the location, size and semantic mask of the nodules. For the classifier part, a 3D dual path network was used to summarize and contract features, and the classification results were given. In order to fully utilize the feature in the original data, the results of the detector were used to sample and mask the original data, and a spatial pyramid pooling layer was added before the classifier to obtain a consistent input scale. The experimental results on public datasets show that the proposed deep learning approach has good performance in the detection and classification of pulmonary nodules in CT images.

Aiming at the problem that the current data compression algorithm of sensor network had the defects of low compression ratio and serious data deformation, in order to improve the realtime performance of data transmission of sensor networks, we proposed a data compression algorithm based on spatiotemporal correlation. Firstly, the original data of sensor network was collected, and the spatial transformation technology was used to analyze the correlation between the data of sensor network in space, and then the noise was removed to reduce the spatial resource occupied by noise. Secondly, according to the temporal correlation of the data of sensor network, the compression sensing algorithm was introduced to compress the spatial coefficient to reduce the data redundancy of sensor network. Finally, the performance of data compression algorithm of sensor network was analyzed by simulation experiment. The simulation results show that compared with other sensor network data compression algorithms, the proposed algorithm can improve the data compression ratio of sensor network without losing the data information of sensor network, obtain faster data compression speed of sensor network and reduce the communication pressure of sensor network.

Aiming at the problem of poor control of highspeed Internet communication coverage, we proposed an optimimal control algorithm for highspeed Internet coverage in heterogeneous environments based on energyload balancing control. Firstly, a node deployment and route detection model of highspeed Internet in heterogeneous environment was constructed, and a load balancing control protocol of an adjacent route was used to optimize the design of route protocol. Secondly, the energy load balancing control algorithm was used to improve the coverage of the highspeed Internet. The simulation results show that the control algorithm can realize the route equilibrium control of the highspeed Internet in the heterogeneous environment, the balance of the network channel transmission and the antiinterference ability are good, and the coverage of network communication is high under the condition of minimum nodes, which improves the load imbalance caused by low coverage.

Aiming at the problems of high transmission delay, low channel utilization and throughput of the binary exponential backoff algorithm, we proposed an adaptive backoff algorithm based on MAC layer protocol. Firstly, the size of the backoff factor was obtained by comparing the system delay median and packet transmission time, so that the backoff window changed dynamically. Secondly, the multiconflict Ethernet communication network model was established based on the maximum number of backoff time slots. The simulation results show that compared with the binary exponential backoff algorithm, the algorithm has lower transmission delay, higher throughput and channel utilization in the multiconflict Ethernet scenario, thus improving the transmission realtime performance.

Aiming at the problem of low accuracy of extracting ontology information from Wikipedia information box in traditional methods, we studied the attribute structured information in Wikipedia information box. Firstly, a set of candidate features was defined to determine the relationship between information box attributes, and the association with categories, lists, articles and Wikipedia information box templates was established. Secondly, using the method of ontology matching to extract the structured information of Wikipedia information box, calculate the similarity of attribute pairs, set the boundary constraints, and construct ontology structure to explain the relationship between attributes and construct a class hierarchy with a certain accuracy. The results show that the proposed method solves the problem of low accuracy of extracting ontology inform
ation, and can extract the possible attribute structure in a given topic article effectively and correctly, and find the reasonable class relationship.

The author proposed a characteristic trend reasoning algorithm for largescale data. Firstly, Hash function was used to extract largescale data samples, Pam clustering algorithm and parallel Kmeans clustering algorithm were used to
 cluster largescale data samples. After obtaining the best clustering results, the dynamic characteristics of large data clustering were extracted. Secondly, a reasoning algorithm based on characteristic trend rules was used to construct a trend rule reasoning model for largescale data characteristics, and a trend rule algorithm was designed by the method of cumulative trend rule, which could infer the trends of largescale data characteristics, and solved the problem of large errors of reasoning results. The experimental results show that the average accuracy of the proposed algorithm for large-scale data characteristic trend reasoning is 9810%, the growth rate of reasoning speed is 50%, and the maximum average reasoning timeconsuming is only 11425 s, which can quickly and accurately complete data characteristic trend reasoning.

Aiming at the problems existing in the analysis and optimization design of the working process of planter, we proposed a coupling method of multiple rigid body dynamics (MBD) and discrete element method (DEM). By  integrating the selfdeveloped  multirigid dynamics simulation software with discrete element analysis software, we developed a new type of CAE software—AgriCAE (agricultural computer aid engineering), introduced the implementation method of the software, and verified the feasibility and effectiveness of AgriCAE software by an example.

Aiming at the problem of multitarget tracking in video behavior recognition, due to the mutual occlusion of the target and the complexity of the environment background, we proposed a method to detect and locate active individuals in video by using a local pattern activity discrimination model, which solved the problem of low recognition accuracy caused by factors such as incomplete trajectory extraction or too complicated background due to occlusion in the trajectorybased method. The model was applied to the video segments of the UEFA Euro 2012 and the 2013—2014 season Spanish League One 38 matches associated with the goal event, and the average accuracy rate was 91.3%. The experimental results show that the method has high accuracy and practicability for the recognition of target behaviors in videos.

Two magnetic flux neurons were coupled by magnetic flux coupling, and the coupled neuron model was established. Firstly, RouthHurwitz criterion was used to analyze the stability of the equilibrium point and calculate the unique equilibrium point of the model. Secondly, the analytic solution of bifurcation was obtained by Hopf theorem, and the bifurcation direction of the model and the stability of bifurcation periodic solution were studied. Finally, the dynamic behavior of the model was simulated by numerical simulation. The results show that, within a certain range of parameters, with the increase of the coupling strength, the model generates a subcritical Hopf bifurcation, and at the same time, the phenomenon of inverted doubling cycle, plus cycle bifurcation and more periodic windows appear, and increasing the external stimulation current can induce the spike discharge.

The response system was constructed based on the state equations of the drive system and the oneway coupling principle of the chaotic system, and the simulation circuit of the generalized modified functional projective synchronization (GMFPS) of the chaotic system was designed. The results show that the sufficient condition of the drive system and the response sys
tem realizing the GMFPS is that the feedback gain matrix is positive definite. The numerical simulation results are same with the phase diagrams of the drive system, the phase diagrams of the response system and the waveform diagrams of the GMFPS on the oscilloscopes. Therefore, it is proved to be correct of the circuit of the GMFPS of the chaotic system.

Firstly, graphene oxide (GO) was prepared by modified Hummers method. Secondly, Ag/GO colloids were 
synthesized from GO and using glucose as reducing agent to reduce silver nanoparticles in silver ammonia solution. Finally, Ag/GO coating was obtained under vacuum drying condition, and Ag/reduced graphene oxide (rGO) coating was prepared
 by vacuum stepby\|step thermal reduction technology. The structure and morphology of the films were characterized by X-ray diffraction, scanning electron microscopy and transmission electron microscopy. The hydrophilic/hydrophobic and antibacterial properties of the samples were tested by wetting angle tester and inhibition zone method. The results show that the graphenebased coatings have a good combination with the substrate, Ag nanoparticles are spherical shape and uniformly distributed between the layers of graphene sheets, and the particle size range is 20—50 nm. No bacterial was observed on the surface of GO and rGO films, and no clear zone of inhibition is found in E.coli and S.aureus. Compared with the Ag/GO composite film, Ag/rGO composite film has stronger antibacterial activity, and low temperature 
annealing is helpful to improve the antibacterial performance of graphenebased composite coating.

The far red phosphorLi₆(La₂Ca)Nb₂O₁₂∶Mn⁴⁺ with nonrareearth doping was prepared by high temperature solidstate method. The crystal structure and luminescent properties of the phosphor were studied by Xray diffraction and
 sepectroscopy. The results show that the fluorescence spectrum of Li₆(La₂Ca)Nb₂O₁₂∶Mn⁴⁺ has two broad excitation bands in the center of 327,494 nm. A far red emission peak of Li₆(La₂Ca)Nb₂O₁₂∶Mn⁴⁺ phosphor can be 
observed at 700 nm due to the ²E_g→⁺⁴A_2gtransition of Mn⁴⁺ ion. The calculated activation energy ΔE=0.437 eV. The phosphor has good thermal stability.

Lithiumrich layered cathode material Li_1.18Ni_0.15Co_0.15Mn_0.52O₂ was synthesized by the solgel method, then surface coated using Cu₃(PO₄)₂. The surface morphology of the samples was measured by X-ray diffraction (XRD), scanning electron microscopy (SEM) and infrared spectroscopy, and the samples were tested by constant current chargedischarge and electrochemical impedance spectroscopy. The results show that Cu₃(PO₄)₂ distributes uniformly on the surface of the material. Cu₃(PO₄)₂ exists in amorphous form and the ordered arrangement of Li⁺ in transition metal layer is destroyed after modification. The initial Coulomb efficiency of the material is increased from 77% to 94% after surface modification. The initial discharge capacity of the all materials is 244 mA·h/g, the specific discharge capacity of the Cu₃(PO₄)₂ modified material is 203 mA·h/g after 100 cycles, and  the capacity retention is 83%. 
A pair of redox peaks appear at 30, 27 V while the charge/discharge curve appear a new platform after surface modification. The impedance of surface modified lithiumrich layered cathode material is obviously reduced.

We synthesized and characterized a new complex of Cu₂(L-Arg)₂(SSA)(H₂O)₂ (L-Arg=L-Arginine, SSA=5sulfosalicylic acid), and studied interaction between complex and DNA by electrochemical method, spectroscopic method and viscosity method with herring sperm DNA as bimolecular target. The  results show that when the scanning rate is 0.1 V/s, a pair of obvious redox peaks appear at 0.124 8,-0.518 9 V,  the redox peak current of the complex increases with the scanning rate, and the reaction of complex at glassy carbon electrodes is controlled by diffusion process. After adding DNA, the oxidation and reduction peak currents of the complex decrease, the formal potential increases, the peak position of the complex shifts,  the absorption intensity decreases, which is positively related to the concentration of DNA, and the relative viscosity of the complex increases. Therefore, there is intercalation between complex and DNA.

Ultrasonic extraction method was used to extract polysaccharides from Cordyceps militaris Link. The optimal extraction process was determined by response surface method. The components of polysaccharides from Cordyceps militaris Link were detected and identified by high performance liquid chromatography. The antiinflammatory effects of polysaccharides from Cordyceps militaris Link was tested by  using RAW264.7 in vitro cell antiinflammatory model. The results show that the optimal extraction process is the  extraction temperature of 65 ℃, ultrasonic power of 1 800 W, extraction time of 30 h, the extraction rate can reach 3156% under this condition. The monosaccharide components are Ara,Gal,Xyl,Man,Glc and Rha. The polysaccharide from Cordyceps militaris Link has antiinflammatory activity.

Using mass fraction of 50%CuO-TiO2 as the catalyst which synthesized by wet impregnation method, we investigated the effects of different illumination conditions, initial pH value of the system and catalyst dosage on the photocatalytic degradation efficiency of four kinds of phthalate esters (PAEs), and detected the degradation process solution of dibutyl p
hthalate (DBP) with different illumination time by electrospray extractive ionization mass spectrometry (EESIMS). The results show that the degradation efficiency of PAEs is the best under the condition of ultraviolet light, the initial pH=6 and the mass concentration of catalyst is 20 mg/L. According to the result of partial least squares discriminant analysis (PLS-DA), we surmised the possible degradation intermediates of DBP, and give the possible photocatalytic degradation pathway of DBP under the optimal reaction conditions.

We studied the changes of structural characteristics before and after kaolinite and montmorillonite participated in the liquid shake flask culture of lignin inoculated the suspension of mixed strains during the culture period of 110 d by using scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR) and Xray diffraction (XRD). The results show that when kaolinite is involved in the microbial transformation of lignin, the structural water is unbalanced, the edge bond breaking makes its surface accumulate negative charge, the surface hydration layer forms hydrogen bonds at multiple points, which increases the stretching vibration of association —OH, the edge and the base octahedron O of Al—OH all have dehydroxylation, which makes the deformations of tetrahedral and octahedral sheets and generate a large number of broken bonds, resulting in weakening of the vibrational frequencies of Si—O,Si—O—Al and Si—O—Si, and the crystal structures change to longrange disorder, but there is no phase change. Montmorillonite is an expanding mineral, which is hydrophilic inside. After the liquid shaking flask culture, the crystal water shrinks to destroy the interlayer structures and increase the surface roughness. After participating in the microbial transformation of lignin, the extracellular polymers released by the microorganism forms a hydrogen bond with the surface functional group of the montmorillonite, which reduces the total amount of the hydroxyl groups and crystal H2O in the interlayer and lattice, increases the vibrational frequencies of Si—O,Mg—Al—OH and Fe—O—Si bonds (or Mg—O—Si bond), and the characteristic diffraction peak at low wave disappears.